Scope magnification is a multiplication measurement compared to the average naked eye. Basically the magnification number determines how many times better you will see an object than with your naked eye. Magnification is typically the first number that you see in scope performance.
For example, a 4X32 scope has a four power magnification which means you can see 4 times better than you could without the scope. A 6X42 scope has a six power magnification and an 8X32 has an eight power magnification.
Here's a graphic image to help explain:
Scopes also come in a variable or adjustable power that offers a range of magnification. With these scope models, there will be a range of numbers (usually going lower to higher) that are separated by a hyphen.
For example, a 3-9X36 is very common hunting configuration. In an adjustable magnification scope such as that, the magnification can be set anywhere from three power all the way up to nine power. Variable power scopes tend to be most popular for hunting applications.
What's the best magnification power? It really depends on your needs, but we'll get into talking about that later.